Determinant Calculator
Calculate the determinant of any square matrix, from 2×2 to 10×10, with ease.
Determinant
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How to Use This Tool
- Set Matrix Size Select your desired matrix dimension (e.g., 3 for a 3×3 matrix) and click “Set Matrix”.
- Enter Values Fill in each cell of the matrix. You can use integers, decimals, or fractions (like `5/4`).
- Calculate Determinant Click “Calculate Determinant” to get the result instantly. If needed, click “Show Solution Steps” for a detailed breakdown of the calculation.
Frequently Asked Questions
The determinant is a special number that can be calculated from a square matrix. It is a fundamental concept in linear algebra, used to solve systems of linear equations, find the inverse of a matrix, and in calculus for variable substitution. A matrix has an inverse only if its determinant is non-zero.
This calculator uses the method of cofactor expansion along the first row. For a 2×2 matrix, it applies the simple formula ad - bc. For larger matrices, it recursively breaks down the matrix into smaller 2×2 sub-matrices, calculates their determinants, and combines them according to the cofactor expansion formula.
Yes. The calculator fully supports integers (e.g., `7`), negative numbers (e.g., `-5`), decimals (e.g., `2.5`), and fractions (e.g., `3/4` or `-1/2`). Our parser will handle these inputs automatically.
